A128165 Numbers k such that k divides 1 plus the sum of the first k primes.

1, 2, 6, 10, 20, 22, 28, 155, 488, 664, 992, 6162, 7840, 7975, 8793, 18961, 32422, 148220, 231625, 332198, 459121, 462932, 2115894, 8108930, 10336641, 11789731, 15500046, 23483195, 46571611, 48582404, 77033887, 105390951, 132421841, 229481560, 1224959312

Offset

1,2

Comments

a(44) > 4.4*10^10. - Robert Price, Dec 15 2013

a(50) > 10^14. - Bruce Garner, Jun 05 2021

Links

Bruce Garner, Table of n, a(n) for n = 1..49

OEIS Wiki, Sums of powers of primes divisibility sequences

Mathematica

k = 0; s = 1; p = 2; A128165 = {}; While[k < 247336000, If[Mod[s += p, ++k] == 0, AppendTo[A128165, k]; Print[{k, p}]]; p = NextPrime@ p]; A128165

Prog

(PARI) is(n)=sum(i=1, n, prime(i), 1)%n==0 \\ Charles R Greathouse IV, Nov 07 2014
(PARI) n=0; s=1; forprime(p=2, 1e9, s+=p; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Nov 07 2014

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248, A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A028247 A209535 A065054 * A097646 A077084 A239542

Adjacent sequences: A128162 A128163 A128164 * A128166 A128167 A128168

Keyword

hard,nonn

Author

Alexander Adamchuk, Feb 22 2007

Extensions

More terms from Ryan Propper, Apr 05 2007

a(34) from Robert G. Wilson v, Jan 21 2011

a(35) from Robert Price, Dec 15 2013

Status

approved